Question
Solve for \( x \) using the square root property. \( 4(p+6)^{2}-27=9 \) \( p= \) Entry Tip: Do not use a decimal approximation for square roots. To enter a number like \( 5 \sqrt{7} \), type \( 5^{*} \) sqrt(7). Preview your answer before submitting! Furthere Tip: Write your answers as a list, with your answers separated by (a) comma(s). For example, if you get 4 and \( -\frac{2}{3} \) as your answers, then enter \( 4,-2 / 3 \) in the box.
Ask by Vargas Nunez. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( p = -9, -3 \)
Solution
Solve the equation \( 4(p+6)^{2}-27=9 \).
Solve the quadratic equation by following steps:
- step0: Solve by factoring:
\(4\left(p+6\right)^{2}-27=9\)
- step1: Expand the expression:
\(4p^{2}+48p+117=9\)
- step2: Move the expression to the left side:
\(4p^{2}+48p+108=0\)
- step3: Factor the expression:
\(4\left(p+3\right)\left(p+9\right)=0\)
- step4: Divide the terms:
\(\left(p+3\right)\left(p+9\right)=0\)
- step5: Separate into possible cases:
\(\begin{align}&p+3=0\\&p+9=0\end{align}\)
- step6: Solve the equation:
\(\begin{align}&p=-3\\&p=-9\end{align}\)
- step7: Rewrite:
\(p_{1}=-9,p_{2}=-3\)
The solutions to the equation \(4(p+6)^{2}-27=9\) using the square root property are \(p=-9\) and \(p=-3\).
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Simplify this solution Mind Expander
To solve for \( p \) in the equation \( 4(p+6)^{2}-27=9 \), we first isolate the squared term. 1. Add 27 to both sides: \[ 4(p+6)^{2} = 36 \] 2. Divide by 4: \[ (p+6)^{2} = 9 \] 3. Apply the square root property: \( p+6 = 3 \) or \( p+6 = -3 \) 4. Solve for \( p \): \( p = 3 - 6 = -3 \) or \( p = -3 - 6 = -9 \) Final answer: \( -3,-9 \)
